Theoretical bounds of majority voting performance for a binary classification problem

A number of earlier studies that have attempted a theoretical analysis of majority voting assume independence of the classifiers. We formulate the majority voting problem as an optimization problem with linear constraints. No assumptions on the independence of classifiers are made. For a binary classification problem, given the accuracies of the classifiers in the team, the theoretical upper and lower bounds for performance obtained by combining them through majority voting are shown to be solutions of the corresponding optimization problem. The objective function of the optimization problem is nonlinear in the case of an even number of classifiers when rejection is allowed, for the other cases the objective function is linear and hence the problem is a linear program (LP). Using the framework we provide some insights and investigate the relationship between two candidate classifier diversity measures and majority voting performance.